Question

What properties of $R$ does the monoid ring $R[M]$ inherit?

score 334 · Answer 1 · 2026-03-25 03:07:27

334

Views

What properties of $R$ does the monoid ring $R[M]$ inherit?

Published on 25 Mar 2026 - 3:07

score 112 · Answer 2 · 2026-03-25 20:42:21

112

Views

Product ring isomorphism from example 11.6.3 in Artin's Algebra

Published on 25 Mar 2026 - 20:42

score 88 · Answer 3 · 2019-02-19 01:36:05

88

Views

Determining number of cosets in a quotient ring

Published on 19 Feb 2019 - 1:36

score 38 · Answer 4 · 2019-02-19 01:46:11

38

Views

$P$ and $Q$ are ideals of ring $R$, $\phi: R \rightarrow R/P \oplus R/Q$, determine $\ker \phi$

Published on 19 Feb 2019 - 1:46

score 328 · Answer 5 · 2026-03-30 14:43:33

328

Views

The degree extension of $\mathbb{Q}(\sqrt{2},\sqrt{3})/\mathbb{Q}(\sqrt{2})$ is at most $2$ because $[\mathbb{Q}(\sqrt{3}),\mathbb{Q}] = 2$

Published on 30 Mar 2026 - 14:43

score 50 · Answer 6 · 2019-02-19 12:07:15

50

Views

Subgroup $(I, +)$ has finite index in $(R, +)$

Published on 19 Feb 2019 - 12:07

score 127 · Answer 7 · 2026-03-25 07:45:44

127

Views

Showing a map from $\Bbb Q$ to the field of fractions of $\Bbb Z 1_{R}$ is well defined.

Published on 25 Mar 2026 - 7:45

score 309 · Answer 8 · 2026-03-25 09:27:29

309

Views

Prove that there is no homomorphism $f:\mathbb { Z } / n \mathbb { Z }\rightarrow \mathbb { Z }$

Published on 25 Mar 2026 - 9:27

score 131 · Answer 9 · 2026-03-30 13:21:31

131

Views

How to prove this isomorphism of a quotient ring

Published on 30 Mar 2026 - 13:21

score 267 · Answer 10 · 2026-04-01 03:39:11

267

Views

Showing that $\frac{\mathbb{R}[x]}{\langle x \rangle}$ and $\frac{\mathbb{R}[x]}{\langle x-1 \rangle}$ are not isomorphic as $\mathbb{R}[x]$ modules.

Published on 01 Apr 2026 - 3:39

score 75 · Answer 11 · 2026-03-25 06:06:59

75

Views

Find the values of $a\in \mathbb{Z}[i]$ such that $(2,1)$ and $(2+i,a)$ form a basis of $\mathbb{Z}[i]^2$.

Published on 25 Mar 2026 - 6:06

score 473 · Answer 12 · 2019-02-22 11:30:27

473

Views

What is the relation between minimal polynomial of a matrix and of an algebraic integer?

Published on 22 Feb 2019 - 11:30

score 194 · Answer 13 · 2026-03-25 11:13:15

194

Views

Finding the submodules of the $\mathbb{R}[x]$-module defined by $A=\begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 &0 & -1 \end{bmatrix} $

Published on 25 Mar 2026 - 11:13

score 91 · Answer 14 · 2026-03-25 06:50:37

91

Views

Is $M=\frac{\mathbb{Z}^3}{\langle (3,3,1),(2,2,2)\rangle}$ free?

Published on 25 Mar 2026 - 6:50

score 904 · Answer 15 · 2026-03-30 13:22:18

904

Views

Product of the two subrings

Published on 30 Mar 2026 - 13:22

List Question

What properties of $R$ does the monoid ring $R[M]$ inherit?

Product ring isomorphism from example 11.6.3 in Artin's Algebra

Determining number of cosets in a quotient ring

$P$ and $Q$ are ideals of ring $R$, $\phi: R \rightarrow R/P \oplus R/Q$, determine $\ker \phi$

The degree extension of $\mathbb{Q}(\sqrt{2},\sqrt{3})/\mathbb{Q}(\sqrt{2})$ is at most $2$ because $[\mathbb{Q}(\sqrt{3}),\mathbb{Q}] = 2$

Subgroup $(I, +)$ has finite index in $(R, +)$

Showing a map from $\Bbb Q$ to the field of fractions of $\Bbb Z 1_{R}$ is well defined.

Prove that there is no homomorphism $f:\mathbb { Z } / n \mathbb { Z }\rightarrow \mathbb { Z }$

How to prove this isomorphism of a quotient ring

Showing that $\frac{\mathbb{R}[x]}{\langle x \rangle}$ and $\frac{\mathbb{R}[x]}{\langle x-1 \rangle}$ are not isomorphic as $\mathbb{R}[x]$ modules.

Find the values of $a\in \mathbb{Z}[i]$ such that $(2,1)$ and $(2+i,a)$ form a basis of $\mathbb{Z}[i]^2$.

What is the relation between minimal polynomial of a matrix and of an algebraic integer?

Finding the submodules of the $\mathbb{R}[x]$-module defined by $A=\begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 &0 & -1 \end{bmatrix} $

Is $M=\frac{\mathbb{Z}^3}{\langle (3,3,1),(2,2,2)\rangle}$ free?

Product of the two subrings

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